{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.4高斯过程"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "先回顾高斯分布相关知识，高斯分布，又叫正态分布，是连续变量经常使用的一个分布模型，一维的高斯分布如下：\n",
    "\n",
    "$$\n",
    "\\mathcal{N}\\left(x\\left|~\\mu,\\sigma^2\\right.\\right) = \\frac{1}{(2\\pi\\sigma^2)^{1/2}} \\exp\\left\\{-\\frac{1}{2\\sigma^2}(x-\\mu)^2\\right\\}\n",
    "$$\n",
    "\n",
    "其中 $\\mu$ 是均值，$\\sigma$ 是方差。\n",
    "\n",
    "$D$-维的高斯分布如下：\n",
    "\n",
    "$$\n",
    "\\mathcal{N}\\left(\\mathbf x\\left|~\\mathbf{\\mu, \\Sigma}\\right.\\right) = \\frac{1}{(2\\pi)^{D/2}} \\frac{1}{|\\mathbf\\Sigma|^{1/2}} \\exp \\left\\{-\\frac{1}{2}(\\mathbf x - \\mathbf \\mu)^\\top\\mathbf\\Sigma^{-1}(\\mathbf x - \\mathbf \\mu)\\right\\}\n",
    "$$\n",
    "\n",
    "其中，$D$ 维向量 $\\mathbf \\mu$ 是均值，$D\\times D$ 矩阵 $\\mathbf\\Sigma$ 是方差，$|\\mathbf\\Sigma|$ 是其行列式。\n",
    "\n",
    "之前我们已经看到，在均值和方差固定时，高斯函数是熵最大的连续分布，因此高斯分布的应用十分广泛。\n",
    "\n",
    "而中心极限定理告诉我们，对于某个分布一组样本 $x_1, \\dots, x_N$，他们的均值 $(x_1+\\dots+x_N)/N$ 的分布会随着 $N$ 的增大而越来越接近一个高斯分布。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "高斯过程就是就是一系列关于连续域（时间或空间）的随机变量的联合(服从多元高斯分布)，而且针对每一个时间或是空间点上的随机变量都是服从高斯分布(但其参数与时间或空间有关)的。[帮助理解高斯过程](https://www.cnblogs.com/hxsyl/p/5229746.html)\n",
    "\n",
    "+ 一个高斯过程可以被均值和协方差共同唯一决定，均值描述了样本出现的整体位置，一般设置为0，但可也可以设置为线性函数。\n",
    "\n",
    "+ 协方差反映了输入数据点之间的相似性度量，引入核函数来计算相似性。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "假定一个没有噪声的高斯回归\n",
    "+ 目标是对$f:\\mathbb{R}\\rightarrow \\mathbb R$建模\n",
    "+ $x=[x_1,...,x_N]^T,y=[y_1,...y_N]^T$\n",
    "+ 预测f在某些未知输入$x*$上的值\n",
    "\n",
    "$$\\begin{pmatrix}\n",
    "y_0\\\\\n",
    "y_1\n",
    "\\end{pmatrix}\\sim \\mathcal N\\bigg(\\begin{pmatrix}\n",
    "0\\\\\n",
    "0\n",
    "\\end{pmatrix}，\\begin{pmatrix}\n",
    "1& 0\\\\\n",
    "0& 1\n",
    "\\end{pmatrix}\\bigg) $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.append(r\"../\")\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "import matplotlib.cm as cm\n",
    "\n",
    "from prml.kernel import (\n",
    "    PolynomialKernel,\n",
    "    RBF,\n",
    "    GaussianProcessClassifier,\n",
    "    GaussianProcessRegressor\n",
    ")\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如下图，每次从分布中抽取10个点，依次次赋予$X\\in [0,1]$中的10个点(空间点或时间点),重复10次就得到了下图。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_unit_gaussian_samples(D):\n",
    "    xs = np.linspace(0, 1, D)\n",
    "    fig=plt.figure(figsize=(8,6))\n",
    "    for i in range(10):\n",
    "        ys = np.random.multivariate_normal(np.arange(D), np.eye(D))\n",
    "        plt.plot(xs,ys,lw=1)\n",
    "    return "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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02mm+Ov4VmYWZLB2+FHO9OWvWruNMeCSnaEiRbXOeHerHgObl91xLVl5PxtVl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\nALVrjvxGJGSIAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f41677e6e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_unit_gaussian_samples(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.4.1 重新考虑线性回归"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "考虑⼀个模型M，它被定义为由向量ϕ(x)的元素给出的M个固定基函数的线性组合，即$$y(x)=w^T\\phi(x)$$\n",
    "考虑w上的一个先验分布:$$p(w)=\\mathcal N(w|0,\\alpha ^{-1}I)$$其中$\\alpha$为超参数，代表精度。记函数值的集合记作向量$\\mathbf{y}$,$\\mathbf y=\\Phi w$\n",
    "\n",
    "y是由w的元素给出的服从⾼斯分布的变量的线性组合，因此它本⾝是服从⾼斯分布,其均值为0方差为$$cov[\\mathbf y]=\\mathbb E[\\mathbf{yy^T}]=\\Phi\\mathbb E[ww^T]\\Phi^T=\\frac{1}{\\alpha}\\Phi\\Phi^T=K$$\n",
    "⾼斯过程的确定通过给定两个x处的函数值y(x)的协⽅差来完成。这个协⽅差由核函数确定:\n",
    "$$\\mathbb E[y(x_n)y(x_m)]=k(x_n,x_m)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.4.2 用于回归的高斯过程"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "已知的输入向量$x=[x_1,...x_N]$,预测$x_{N+1}$处的$t_{N+1}$\n",
    "$$t_n=y_n+\\epsilon_n$$\n",
    "$$p(t_n|y_n)=\\mathcal N(t_n|y_n,\\beta^{-1})$$\n",
    "目标值$t=(t_1,...,t_N)^T$的联合概率分布时一个各向同性的高斯分布\n",
    "$$p(t|y)=\\mathcal N(t|y,\\beta^{-1}I_N)$$\n",
    "边缘概率分布$$p(y)=\\mathcal N(y|0,K)$$\n",
    "为了找到一输入值$x_1,...,x_N$为条件的边缘概率分布$p(t)$需要对y积分：$$p(t)=\\int{p(t|y)p(y)dy}=\\mathcal N(t|0,C)$$\n",
    "\n",
    "已知：\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "p(\\mathbf x)&=\\mathcal N(\\mathbf x~|~\\mathbf \\mu, \\mathbf \\Lambda^{-1}) \\\\\n",
    "p(\\mathbf y|\\mathbf x)&=\\mathcal N(\\mathbf y~|~\\mathbf{Ax+b}, \\mathbf L^{-1}) \\\\\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "我们有\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "p(\\mathbf y)&=\\mathcal N(\\mathbf y~|~\\mathbf{A\\mu+b}, \\mathbf L^{-1}+\\mathbf A\\mathbf \\Lambda^{-1}\\mathbf A^\\top) \\\\\n",
    "p(\\mathbf x|\\mathbf y)&=\\mathcal N(\\mathbf y~|~\\mathbf \\Sigma\\left\\{ \\mathbf A^\\top \\mathbf{L(y-b)} + \\mathbf{\\Lambda\\mu} \\right\\}, \\mathbf \\Sigma) \\\\\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "其中 $\\mathbf \\Sigma = (\\mathbf\\Lambda + \\mathbf A^\\top\\mathbf L\\mathbf A)^{-1}$。\n",
    "\n",
    "协方差矩阵$$C=(x_n，x_m)=k(x_n,x_m)+\\beta^{-1}\\delta_{nm}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "接着计算预测分布$p(t_{N+1}|\\mathbf t_N)$,先找到联合概率分布$p(\\mathbf t_{N+1})=\\mathcal N(\\mathbf t_{N+1}|0,C_{N+1})$\n",
    "$$C_{N+1}=\\begin{pmatrix}C_N&k\\\\k^T&c\\end{pmatrix}$$\n",
    "其中$k=k(x_n,x_{N+1})$,n,m=1,...,N$,c=k(x_{N+1},x_{N+1})+\\beta^{-1}$,\n",
    "$p(t_N+1|\\mathbf t_N)$也为高斯分布,\n",
    "均值为$$m(x_{N+1})=k^TC_N^{-1}t$$\n",
    "方差为$$\\sigma^2(x_{N+1})=c-k^TC_N^{-1}k$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "回到例子，我们用Sqared Exponential kernel来定义来计算协方差矩阵$$k(x,x')=exp(-\\frac{(x-x')^2}{2})$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7f4162ae3668>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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WQ8WZedoYPpg3JjWuLhcf52kzm7RekWlvRoYzMynz211kZgclnQbcJelRM7t3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\nOBm4gXQcx8nADaTjOE4G/x8Cl2lXESsqogAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f417160b128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def k(xs,ys,sigma=1,l=1):\n",
    "    dx=np.expand_dims(xs,1)-np.expand_dims(ys,0)\n",
    "    return (sigma**2)*np.exp(-((dx)**2)/2)\n",
    "def m(x):\n",
    "    return np.zeros_like(x)\n",
    "\n",
    "N = 100\n",
    "x = np.linspace(-2, 2, N)\n",
    "y = np.linspace(-2, 2, N)\n",
    "d = k(x, y)\n",
    "#绘制协防差矩阵\n",
    "plt.imshow(d,origin='lower',extent=[-2, 2, -2., 2.],vmax=abs(d).max(), vmin=-abs(d).max())\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 1],\n",
       "       [1, 1]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.expand_dims([2,2],1)-np.expand_dims([1,1],0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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i3rlkgxBDWR2Va9OpO1WG46BAPO7uiMqqZbqdKYrC4cOH2bBhA9HR0UycOBEr\nK6tLn3gNkMQshBBN0GrPkJL6DjXV6YSHv4C39yiz1r7W5+RQ8Pob1B49iveLL+I6cULjeCqyG94h\nJ6+HAc/CpG8vKH0y6I2c2J7HwXWZ+Ld3bXIEo8lk5PTObST8soBKa1cWdBtPSQdf7Or28YybLdNu\nehl7q4tvpjJq66na3NAcxMrPAUVvQm1l0WJJuby8nBUrVlBbW8t9992H3/ndy65xkpiFEOIP6nQF\npKXNpaRkM6Eh0+je7TPU6itrcHElTHV1lH75FeXz52PbrRumykpMFeXnknJNGex8Hw7Nh5hHGkqf\nbBvPcjYaTZzelc+B1Rl4Bjkx9qkeeAY2rudVTCaS9u4iYdECqhQrFgeNIDfKH0UpYKzNDl6Nux8f\nh/PKri6I1UDVjlyqd+dhH9XQHASVipoDhdjHXPzcy/pemEzs27ePbdu20b9/f+Li4rCwME+/8atJ\nErMQQgAGQxWZmV+Qk/sjAQF3Edd3I1ZWLVO+81coikLVxo0UzXwH227dCF36Kyo7Oyp//RWXiROh\nvgb2fga7P4bIcTBtDzj5NrqGyaSQvK+AfSvTcfa045a/dcU3zOWC+6Qd3E/Cz/Op1BlY49mPjJ4B\naG1VdDPtZHbMeDp7TLp4rHoT2j15Dc1BOrjh/URPLN3PPa07DbpwGtWfVVRURHx8PGq1mkceeQRP\nT88rvmZbJYlZCHFDM5nqyc1bSEbGPDzcb6JP7ApsbS+s7W1NurR0Ct96C31BAX5vTschLu73r3k8\n+AAcng9b32nYYf3wevBsvBFNMSmkHipm34o0bB2sGHJfZwI6Nu4LrSgKWceOsPPnH6jQaEnw6MvJ\n3kGUuDvgo9vF3PbRDA9+6aLL94pRoeZgIZqNWVgFOOL1aDesfK+8OcgfGQwGEhIS2Lt3L4MHDyY6\nOrrNDZ1oaZKYhRA3JEVRKC5eR0rqu9jZBRPV41ucnDqbNSajtprSzz6lYvESPP7+d9zvnYLqtw1N\nitJQi7z+FfCIgMnzITC60fmKopB5vJS98WmoVCr6T2pPcOSFIxhzTp8g4ecfKC0q4bBXHw72CqEk\n2B6r+tP8y9eZv3V+Cit18xupFEWh9ngpmvUZqB2tcZ/SqcWag/xRbm4u8fHxODk5MXXqVFxdL+xO\ndj2SxCyEuOFUVh7mzJnX0NUX0qHDf/HxHmnWeBRFQbNyFUWzZ+PQt29DG80/lj9l7YUNr0B5BtSU\nQL+nLkiyZE9xAAAgAElEQVTKOafL2BufRn2dkT5jwwiNurBGuCA1mYRF8ynMzCQ5oB87Og2hLtKK\nKqOW2x2yeG3gJJytL55g65LLG5qDmBRcx4Zj075lmoP8UX19PVu3buXIkSPccsstdOvWrU0PnWhp\nkpiFEDeM2tpcUtNmUVG+DxfXaKq0x6irzTZrTHVnzlA4/U2M1dUEzHkf+169zn2xJAU2vQa5h2DI\nvyFiWMNTc9S9vx9SkFbJnuWpaMt0xI4NJSLGB/V5IxiLszLYtWgBuclnyG3XnzXt+mEfo6ZAbUO0\nxUk+7D2ads5BF42zPruKynUZGCt0OI842xxE3fLJMiMjg/j4ePz9/XnsscdwdDRfRzVzkcQshLju\nGQxaMjI/Izf3J4IC76dzp7cxGutwduqGn98dZonJqNFQ/OFHaFavxuvJJ3C9805Uv+0w1hbB1plw\nclnD0/HEL8HqbJ1x/6cBKM6qYm98GqV5WnqPDqVjX18szhvBWJaXy+7FP5Jx7Ajl4f1Z6n8X/tE2\nFFna4mc6xcLIGAb4/eOiceqLatCsy6A+uwqnYcE4RPugsmj5d7x1dXVs2LCB5ORkRo0aRadOnVr8\nHtcKScxCiOuWohjJy/uFtPS5eLgPpE/sSmxtG2peLSzsadduauvHZDJRuXQpRXPm4jRkCGGrVmLp\ndnZjlk4Lu+fB3k+hxz3wxAGwb9x7uiyvmn0r0shPqyT61hBG/r0bFlaNE2VlUSG7l/xEauI+ajr0\n52f/u+jY1YlKewWNvpA3At15qMMjF10eNlTUodmQRd3pMpxuCsT9rpZrDnK+pKQkVq5cSUREBNOm\nTcPW9srHPV7LJDELIa5LZWUJJCe/haWVCz26f4mzc7dLn3SV1R47RsH0N0EFQZ99hl3Xs127jAY4\n9EPDU3LIAPjbFnAPbXRuZXEtu5emknmihKhhwQx96MIRjNqyUvYsXcTpXdsxderHj4H30DXcHbW7\nhu2Geu5y0TC9xzhsLZtPfEZtPVVbsqk5VIRDHz98X4hBbXd1UkV1dTVr164lJyeH8ePHExZ26X7b\nNwJJzEKI60p1dQrJKTOpqUklIuIlvDxHmH3jkKGsjOI5c6jauhXvZ5/DZfw4VGr12SETaxp6Wjv6\nwN0/NUx/+oPqCh0HVmeQnFiIV7ATBp0JKxuLRkm5RlPJvmW/cHzrRiw79WVRuylE+Hni3a6M1fUm\n+liWE99nBL72Hs3GaNIZ0O7IRbsrD7seXvg8G42F09VprKIoCsePH2ft2rV0796dxx57DGtr8zVx\naWskMQshrgv19WWkZ3xIYeEqQtr9g+7d5qFWm3fCkGIwUP7zz5TM+wTnMaMJX7UKC+ezu55zDjSU\nPtWWw4i3LhgyUafVc3BdJicT8ujc358pr/cF4NSufDr38zt7jJYDK5dyZMNqbDvFsDLiXtzcPejS\nRcuKmnr89VqWde9ArNeA5mPUm9Duzadqaza27d3wfjwKSw+7Zo+/UpWVlaxatYqKigruvvtuAgOv\nvPnI9UbGPgohrmkmk47snIZRjD4+owkNeQpr64vPBG4NNYmJFEx/EwsnJ3xe+Q+2Hc7OPy5NbRgy\nkb2vYchE1D2NhkzU1xk4simbo5tzCI/2JmZkyAUTn+prazi4Op6Da+Jx6BBFvCoSvZ0rfWJVfFel\nwaSY+G+YJ/eH9Wk2PsWoUHPobHMQPwdcbglp8eYgf2QymTh48CCbN28mNjaWAQMGYGl54zwbythH\nIcR1r6FByHpSUmfiYB9BdK+FODiEmzss9IVFFM2eTc3+/fi8+H84jRzZsJReXQLb3oFjiyHucRj/\nKVifGwZhqDdyfHsuB9dlEhTpzh0vRePi1XhYhKa0mE1ffkJ+yhmcI7qyr+u9ZBntuXOgK99Xp/Gp\nxoN7PC15q9tgrCya/vGuKAp1J0qpXJ+B2t4K97s7YdPu6rYeLS0tJT4+HoPBwIMPPoj3+SMqRSOS\nmIUQ1xyN5ijJyW9jMFbRqeObuLv3N3dIKPX1lP0wn9Ivv8R10iTCV61E7eDQ0NN6zzzY/UnDCMYn\n9oPDuT7Pfxww4RXsxLhneuIR0Lh216DXc2zTWnYu/J762lrKQuP4QenD3/r4s9Z0kjeqrOhjZ82y\nntF42zVf91uXUtHQHMRgwmV0GLYd3K7q+3ej0cj27dtJSEhg4MCBDBw48Lpvp9kSJDELIa4ZdXX5\npKa9R1lZAmFhz+DvdwcqlfmnC2kTEih8622sAgJo99OP2ISGgskIB7+HLTMguA88uhE8zj3RKyaF\n5MRC9sWn4+Rhyy1Tu+Ibet5UKIOBE9s2smfJzzj5B5HV806ykpKJ7T+CmwMKeLU0Bz8rO5ZFhRDr\n0fwvJ/U5Dc1BDGV1uIxoh103r6vSHOSP8vPziY+Pp66uDoPBgKWlpSTlyySJWQjR5hmNNWRmfkF2\nzg8EBtxNXN8NWFqavyOUPjeXwnfepe7kSXz+9TKOgwejAkhaBxteBTs3mPwDBJ57tagoChnHStm7\nPA1LazWDpnQkqFPjd+Imk5FTO7aye8lPOHj4UNZnMp9kqulk78i+0BL2W6WhqvDkzfY+PBDSpfn4\nimvQrM9El6nBeUgwDr2vTnOQRvfU69m2bRsHDx5k+PDhdOjQgcOHDxMVFXVV73s9kc1fQog2S1FM\n5Bf8SlraHFxdYwkPewE7uwBzh4VJp6P0f/+j/Lvvcbv/PjweeQS1rS3kJjYkZG0RDH8dOtzaaKd1\nzply9ixLRa8z0ndcGCHdG/ezVkwmzuzZye5ffsTGyZmKzkP5X4qaEV18GNxL4aWkw+RbdORWpxo+\nj74Z62aSrKFSR9XGLGpPluA4MBDHfv6ora/+ykJGRgYrVqzAx8eHkSNH4uTkdOmTbhCy+UsIcc0r\nL99DcvLbqNXWdOv6MS4uPc0dEoqioN2ylcIZM7Dt1JGQJUuwDgyAsnRYOR0yd8HNLzX0sv7D5qvC\ndA17lqeiKa2jTxP9rBVFIeXAHnYtWoCFlTVWAyYyL8mCSL0LH97nyvuZ2/k+tT0uln4oKlugtMmk\nbKzWU7U1m5rEQhxi/fB9Pga1ffNTolrKb+00k5KSGDVqFJ07m3dK17VOErMQok2pqUknJeUdqrSn\niAh/EW/vUWZvEAJQn5FBwYwZ6LOy8X31VRwH9IfqUljzEhxdCH2nwW0fgfW5kqPSPC374tMpzNAQ\nMyqEzv39GvWzVhSFjMOJJCxagMlkxGXgbXyWaoNDkRUzJwWxtGwLdyd54Gsbxq89O+NlBdNP7eWV\nzo3LoEw6I9qduWgTcrHr7oXPM9FYOLdOw47Tp0+zevXq39tp2tldvRroG4UsZQsh2gS9vpL0jI8o\nKFhGcPDfCAp8EAsL8zYIATDV1FDy2edULFqEx98exf2++1CpjLDnU9j1EXSdCIP+CY7nSoAqi2vZ\nvzKdrJOl9BzRjm6DArA8byk56/gREn6ej66mmoCh4/k624kirY7nR0SQptrL3Gwt2EbwakQA9wa2\na/KXE8VwtjnIlmxsIlxxGd7uqjYH+SOtVsuaNWvIz89n7NixhIaGXvqkG5gsZQshrhkmk57c3AWk\nZ8zD2/tW+vZZi7W156VPvMoURaFq7VoK33kX+5gYQpcvw8rLE44shC1vQUA0PLIBPCN+P+e39pkp\niUV0GxzIvW/EYX1en+nc0ydJWDSfqtJiOtx6OwvLPPn0cAVPD/XHySuVf59ZQolNH+5v58B/OnbB\nrokla8WkUHOoCM2GTKx8HfB8uCvW/q2zGU5RFI4cOcKGDRuIiopi/PjxWFld/eXyG4kkZiGEWSiK\nQknpZlJSZmBrG0ivnvNxdOxo7rAA0CUnU/DmWxgrKgiY1ZCYSdkES/4LNk5wxzcNJVBnnd8+857X\n+2Dn2HgpuSA1mYRF8ynLzabr6DtYWxfAx/sLeWSACw8MtuTfxxdyWhtHnFccq7pG4W974VK0oijU\nnSxraA5ia4n75I7YnFdidTWVl5ezYsUKampqmDJlCv7+/q127xuJJGYhRKurqjpJcsrb1NeX0KH9\nK3h4DDJ3SAAYq6oo+fhjKuNX4Pn447jdNRlV0XH4fhxocmHY69Bp9O87rc9vn3nXK30uaJ9ZnJlO\nwqIFFKYl03PsHWT3uotpe7MZ39OS+f/owOxTvzD7eEd87QexpGsksa5Nd+HSpVVQsSoNo6Yel9Fh\n2PfwarV37yaTib1797J9+3b69+9PXFwcFhbmrx+/XkliFkK0Gp2uiLS0OZSUbiY05Cn8/SejVpv/\nx5BiMlG5PJ6i99/DcdAgwlauwFKtheWPQfq2hnfIve4Hi4Yl28tpn1mak82uxT+Se+o4vcZOpCpu\nMk9sy6RvWB0Lpvbgl6zFjDtgjcr+Jt7q0o67/X1QN5Fo63O1Dc1BSmqxDnJCn1uNqbK+1ZJyYWEh\n8fHxWFpa8uijj+Lh0fyEKtEyzP9/hBDiumc01pKV9T+yc77F328ScX03YmnZNmpca0+coHD6myhG\nI0Hz5mEXEQg73oPDCyD27zDm/Yblay6vfWZFQT67F/9I+pGDRI8ej3rgZF7akoG/axlf3B9FomYt\nk/avQes4jPvDPXgpPAQHywufPg0ltVRuyESXVonzkCAcevti0hmx9nfEPsbnqn9fDAYD27dv58CB\nAwwZMoRevXpJ565WIruyhRBXjaKYKCxcQUrqLFxcehIR/n/Y2QWbOywAdOnp5L30MvXZ2fg89ywu\nY0ehOvAlJHwAnW9rqEd28gUubJ/ZZ1zYBe0zNSVF7FmykOT9e+h161iULjcxa0sGOr2Jf97akVrr\nQ7x2fDOFDmPo4+rKO5070M7uwl3nRo0OzaYsao+V4DgwAMf+Aa3SHOSPsrKyiI+Px8PDg9GjR+Ps\nfHWHXNwIZFe2EMLsKioOkJz8FgBdu8zF1fWyfiZddYrJROWvv1Lw9gyUmho8H38c1/YG+CQW/HrA\nQ2vBq2FE4+W0z9SWlbJ32SJOJ2ynx/CRDPrXe8zdkcPp+DO8MKIjwX5FvHZoJqetbsbdYzILOneg\nn9uFO6hNNXqqtuVQvb8A+xhffJ6PwcKhdXc763Q6Nm3axMmTJxk5ciSRkZFtoob8RiNPzEKIFlVb\nm0VK6iwqKw8REf5/+PiMRaVqG0ugdWeSKHjtNRSjEa9nn0G3Ix4Xq21YOtnD8OnQLu73Yy/VPrOm\nsoJ9yxdzYutGugweTrvBo/l0TyGbThXx2M3h3NxVxXuHv2RrXTuM9jG8EhHMPf6eWJyX6Ez1RrS7\n8tDuyMGuiydOQ4OxdGn9+u2kpCRWrVpFaGgoI0aMwN7e/tInicsmT8xCiFZnMFSRnjGP/PzFBAU9\nRGTnd7GwaBtdoEzV1RR/PI/K5cvxeupJXAd2RrXhXzgqJ+Hm6RA15fed1pdqn1mrreLAil85unEt\nnfoPYsKbH/D9kXKe+foo98QG8+uTPfjhzDeM31FLjfMEpoT78H9hATif9x5ZMZqo3l+IZnMWNu2c\n8fpHD6y8Wj8ZVldXs3btWrKzs7ntttsIDzf/TOsbnSRmIcQVMZkMZGV/TUbGR3h6DqdP7GpsbLwv\nfWIrUBSFqg0bKJwxE4fY3oQt+BzLI5/Cj/+BwFioLYOaUlCpGrXP7D06hE79GrfP1NVUk7hqOYfW\nraR9bByT35rDsuQaXvzfUYZ19iH+iT5syF3ChM0HqHafQlSQB291DCHC3rZxTCaF2mPFVK7PxNLd\nFs/7I7EObP2NcIqicOzYMdatW0f37t2ZNm0a1tat08ZTXJwkZiHEX1ZWvpvkpOkYjDUYjTU4OXZq\nM0m5PieHgunT0efk4j/9vzjUJ8CiMRD9IDyZCEYDHO5DZdAk9n9z8vf2mcMfjmzUPlNfV8fBtStI\nXLWM0Kho7p4+m635JsZ9e5LOfs78+LdYkmt2cN+22VS4TMbW9x982jGEIR6NN0wpikJdUjmatRlg\nqcZtQntsI1xb95tyVkVFBStXrkSj0XDPPfcQEGD+iV3inBZJzCqVyhX4CugKKMDDiqLsbolrCyHa\nntrabJJTZlBVdYL2Ef/CxSWGgoIl+PndYe7QUOrrKf36G8q+/Rb3Bx/A46EYVDunQtjN8Pft4Nqw\nK7w0V8uWnf2pKEyh+5CgC9pn6ut1HN2whn3LFxMU2Y3Jr87geI0dUxadxtZKzZzJUajsUnn5wFNk\nWt9ElcezvBgWyAP+nlipG79H1mVqqFybjkmrx+WWEGy7eJhlU5XJZGL//v1s27aNvn370q9fPywt\n5fmsrWmRzV8qleo7YIeiKF+pVCprwF5RlIrmjpfNX0JcmwyGajIzPyM37yeCgh4iOOgRLCxsL31i\nK6nes5eCN97AOjgYn3sGYn10bsNwiRHTwb9hbGRdtZ5D6zM5sjkHo95E79EhxI4N+/0aBr2e45vX\ns3fZInzC2tP/zikUWLgzY80pCirrePHWjrQPqOG9g3PZW+uJxmkME329eTHUDw/rxklOX1BN5boM\n9HnVOA8Pxr6nDyoL8+xyLioqIj4+HpVKxW233YaXl5dZ4rhR/ZnNX1ecmFUqlQtwGAhTLvNikpiF\nuLYoikJB4XJSU2fh5tqH8IgXsbXxNXdYvzOUlFD4zrvUJB7A9x9341i9DFV1UcNO6w63gEqFvt7I\nsS05HNqQRVgPT7oNDiTrZBmd+/lh52iN0WDg5PbN7Pl1Ie4BQfSfNIV6t0BmrT/D3rRSnh7WnmFd\n7Pn82Kcsz8/G4Pkw4U4evNU+iM6OjTe5Gcrq0GzMpC6pHKdBQTj29UNlZZ6d6QaDgZ07d7J3714G\nDx5MTEyMNAoxg9ZOzFHAF8BJoAeQCDytKEr1ecdNBaYCBAcHR2dmZl7RfYUQrUOjOUpS0huYFAMd\nOryCq0u0uUP6nWI0UrFoEcUffoTLqGF4ReShzt1+toXmA2Bhiclo4tSufPavysA31Jk+48Jw8z03\nM9lkMnI6YTu7F/+Ik4cX/e+8F9vAcD7anMLyw7k83D+Ue+J8+SV5Ad8krcPS5zHqLf15o30gt3q6\nNFqSNmrrqdqcTc3hIhzi/HEaGIDa1nxLxTk5OcTHx+Pi4sKYMWNwcWm9gReisdZOzDHAHqC/oih7\nVSrVB4BGUZRXmjtHnpiFaPt0umJSU2dRWraD8PDn8fOd2GbqkaGhlWbBa6+jslTjO9IX2/xl0PtR\n6P802DihKAqpB4vZG5+Gg6s1ceMj8Ak9tyFLMZlI2ruLXb8swNbBkf6T78WzQxf+tyOdrxPSGRcV\nwLTBoSQUrOODI1+i9riXXMsuPBHsy9QgL2z+8NRpqjNQtSOX6t152Ed54zQkCAtH8+1wrq+vZ/Pm\nzRw7doxbb72Vrl27SqMQM2vtOuYcIEdRlL1n/7wYeKkFriuEMAOTSUd29rdkZn15tq/1+jbT1xoa\nJkAVf/AhmjWr8Z4Qg4tpNSrnETAuAVwadhdnny5jz9JUTCaFgZPbE9TZ/ffEpCgKqYn72PnTd+hq\nqhl03yOEx/ZnUWIOH87eSu8Qd5Y93p/cuiP8fct9aGz7UOTzNiM83fkpzA8fm3PduBS9Ce2ePKq2\n5WDbwQ3vJ3pi6W7ed+4pKSmsXLmS4OBgpk2bhoODw6VPEm3KFSdmRVEKVCpVtkql6qgoyhlgKA3L\n2kKIa4iiKJSUbCI55S0cHDoQE/0L9vah5g7rd4qioFm9mqJ33sWxewhh42ux9M6AEb+CbzcAijI1\n7F6aSlVpHX3GhRHRyxuV+lxCzjhykF2L5mPU6/EJa8/J7Zs4cDyNabtN+Drb8uX9MdjYF/J24nOc\nrrVE5/EyXrbO/Ng+kCjnc80/FKNCzcFCNBuzsApwxOvRblj5mjcB1tTUsG7dOjIyMhgzZgzt27c3\nazzir2uplx9PAgvO7shOAx5qoesKIVqBtjqZ5OS3qKvLp2OH1/HwuMncITWiS0+ncPp0DPk5BAxT\nY++ZBMPfhYihoFJRUVjDnuVp5KdW0Ht0KJ37N24OknX8KAmL5lNXpaHfnVPo0Kc/Gw6mcSylno3l\n3vx3fCSdAk3MO/wem/OO4RT4LFUOnvw33J9x3q6NnrbrTpRSuS4DtaMV7vd0wqadeQc8KIrCiRMn\nWLt2LV26dGHatGnY2LR+S0/RclokMSuKchhoGx3qhRCXTa+vJC39AwoLVxAa8jgBAVNQq1t3cMLF\nmHQ6Sj//gvIF8/Ho54Z75yxUQ//V0EJTbUF1hY59q9JJO1hM1PAghj7QGSubc81Bck+fJGHRfKpK\ni4m74x469b+JjNJa/rHgILtTS9HYdOW53sEcq/mZf61Yil/QU5T6TmK8rxePB/tg/4fkXpdSQeW6\nDDCYcB0Thk0HN7O/t62srGTVqlWUl5czefJkgoKCzBqPaBlSWS7EDUhRjOTm/Uxa2ly8vW+hb5+1\nWFt7mDusRrQ7dlLwxmvYukPoLYVYDZkI/Z4Aa4eztcjpnNiZR2Q/f6a80RfbP0xiKkhJImHRfMry\ncuh7+110uWko5bUGXl9xihVH8/nbwDBeGd2RdxK+Z3HxLPws7qI6cC5ers5sDPcn0Pbcxq36nCoq\n12VgKKvDZUQ77Lp5/b48bi4mk4nExES2bNlC7969ufPOO6VRyHVE/ksKcYMpL99DUvJ0LC1d6Bn1\nHU5Onc0dUiP6wkIK336buoN78I0qxXH4KBg8H5x8G2qR12X+Xot8139icXQ7t9mqKCONXb8soDAt\nhT4TJjN+yHD0iprPdqTz5fY0xkUFsOHZmzhctpO/b30KrYU/6nbvU27pwBcRAfRxPTeOUV9cg2Z9\nJrpMDc5DgnHo7YPKwvy70ktKSlixYgUGg4EHH3wQb++20QJVtBxJzELcIGprc0hJmYmm6igRES/j\n7XWr2Zdi/0gxGCifv4CSeR/i2l6H/yMdUY/6Frw7N9Qi78j9vRZ54gu9GtUil+ZksWvRAnLPnCR2\n3B2MefqfqC2tWHY4l9nrztAjyJVfp/Wn0pTMszv+RpkBKtz/QZrBg9HqXL6IHoP67PfCUKmjalMW\ntSdKcBwYiNukDqitLZqJuvUYjUa2bt3K7t27uemmmxgwYIA0CrlOSWIW4jpnNNaQkfkZubk/EhT4\nIJGRs9tUG02A2sOHyf/3P7GoL6TdBDtsJs+G8MFnS5uKfq9FHvn3bo1qkcvzc9m9+Ccyjh4iZswE\nbp32LFa2tiSklPD26lNYW6r58O6euLtV8MHBf3Os9Azhof8ktcaD9vaWpGp0dPLwR61SYazWU7Ut\nm5oDhTjE+uL7fAxq+7bxvv23RiFGoxGDwYCFhYUk5euYJGYhrlOKolBYuIKU1HdwdY0ltvcKbG39\nzB1WI8aKCopmvI528ya8Y/Q4T30FVY+7QK0m+1QZu5emoigX1iJXFhWwe8lC0hL30WvkbQx7dBrW\ndvYkFVYx46ejpBZX889bO9E73IJPj37Exj2biI54lgqbRzHZOLA20h9HCwsWFpRxp4cLms1ZaHfm\nYtfNE59nemHh3DZ2Net0OjZt2sTJkye55ZZbCAsL4/Dhw0RFRZk7NHEVtcgQiz9LOn8JcXVpNEdJ\nSp6OyVRPh/av4OratoomFEWhctECimbPxjmgGq9/PIjFkGfB2v6itchVpSXs+XUhSXsSiBoxiujR\nE7B1dKRIU8ecjUmsP1HI44MjmBDtyYLT37HwzEL6hj7ACYsBGBU1r7cPIO7se2TFYKJ6fwGazVnY\nhLniPLwdVp52Fwu7VZ05c4ZVq1YRFhbGiBEjsLe3v/RJos1q7c5fQog2QqcrJjVtNqWl2wgPex4/\nv9vbVBtNAN3pExS8+CSm0lyCHh6A3X0zwdHrbC3y8SZrkasrytm7bBGndmyl25ARPDTnM+ydXaip\nNzB3YxLf7cpgUkwQ657tz/rsZUyI/4Io/2F0jPyKjVVGXgr25k5fd9QqFYpJofZoMRVrM1BZqnGf\n3Mlsc5GbUlVVxZo1aygoKGD8+PGEhYVd+iRxXZHELMR1oKGN5ndkZn2Bn98dxPXd0KbaaAKYtFpK\npj9HxbodeA4OwO2LZah8O6Mt17F/wekma5FrNJXsj1/C8c3riRw0lAff+wQHVzeMJoWF+7KYszGJ\nvmEeLH+8PyerdnD/+ufxdw4jrtvHLCtVeMDRhQ8jvXGwtEBRFGpPl6FZm4HKWo1tBzdq9hWgz9W2\nicRsMpk4dOgQmzZtolevXkyYMAErq7bxjlu0LknMQlzDFEWhpHQzyclv4WAf3ubaaP6m6qd5FM75\nBDs/a0L/N+v/2bvv8KirrIHj30nvvfdegYQeOkiPSgdRUQEVEdbuqitSBRFF1wIo9oodRUIKvYQA\nIQQCCemV9DLpyUym/N4/IigLrrvvQiYJ9/OXj8/MnTMhmTO3nHswHHhHZy3yz3nXrUVWtLSQErOT\ntH1xBA8fzf2bt2Bp54AkSRzKrmZjbCa2ZkZ8eP8glAa5PH/iITRoGRO2lu/kZgyWzNk72A3P3+qR\nlcVNNMYVom1TYT3ZB5Mwe7RtagztTTEb5KzLHw0ANTU1xMTEoFaruf/++3Fx6T4tNYWuJxKzIPRQ\nra155OSuR6EoJzhoNfb2Y3Qd0jVU6UlUrniajspGXB9/APN7nkOllkj9k1pkZVsbqbG7SI3fTcCg\nKO579W2sHDvrdDPKG3klNpOKRgX/mBqKl0sDb6e+SEFjAdFhzxDf6s2hFng/zI0hv+0jqypbaUwo\nQlXRitUEb8z+sF+tb26I5RgP3fxgfvPHXsljx45l8ODB4rS1IBKzIPQ0KlUjhYXvUFn1Kz4+y/Bw\nX9CtrtEEkBoqkb/8KHX7M7GdOgT3HVuQTCzIOF5x3VpklUJBavxuzuz5Bd+IAdyzfjO2Lm4AlDe0\ns3lvNsdya3l8fCBjwwzZfv5djl04xpywZWhcnuXT+nZe9HNgtrMtejIZarmCpv3FKHLqsRzjif09\nocgMu1fCKykpYffu3dja2rJ06VLRK1m4QpzKFoQe4vI1moWFb+PoMBE/v6e63TWaqNpp+2IlFR/u\nxhDj98kAACAASURBVNDFBZdX38UwuO+f9kVWdSg5vy+O5F0/4hHWl+Fz7sHeo/O+52aFivcO57Mj\nuYQFQ725e5gD3+V+zs7cncwInE+71Z3sqGxikYcDy72cMNfXR9PSQfOhS7SdrcZ8mBuWo9zRM+le\n8w+FQsH+/fvJyspi6tSphIWFdauLXoSb4785lS0SsyD0APX1p367RtOSoMCVWFqG6Tqkq2m1qI9/\nSvXrm2mtNMT5uWewnH0/pVn1V2qRh830v1KLrFapuHAwgeRffsDFP5Dhc+/F0btzb1yl0fJNcgnv\nHMhjXLAjfxvvzeGKXXyS/gljPcbh4f4A28rbGG5jwYt+rribGKFVqmk+WkbriXLMIp2wHOeJvqXR\nXwTd9TIzM4mNjSUwMJCJEydiatp9yrOEm0uUSwlCL9HeXkZe/qs0NaUREPACTo5Tu93sSso/jHzj\nU9ScVGA9YTh+O96hrk7DobfPXVOLrFGryThygJM7v8XB05sZf1+Js19A5ziSxN6LVWyKy8Ld1pTP\nFg2iUHGMJQefI8guiCdGfMD2StCvU/FRuA8Drc2R1FqaE8toPnwJk0BbnP7WHwO77nWrGUBTUxOx\nsbHU1NQwe/ZsfHx8dB2S0I2JxCwI3ZBG00Zx8QeUln2Fp8cDhIW+3u2u0aQmB+WO56j4OQdVuyGS\nGhSm5uzbUXhNLbJWq+HikcOc/OlbrByduOOJ53AL+r15xtmSejbGZtGkULHqzjAMLXJZc+YhjA2M\neXLoRn5usmNDSSsr/N2Y6WQDErSeqaJpXzGGLuY4PNgXI1fzfxOsbmi1WlJSUjh8+DCDBw9m9uzZ\nogRK+EsiMQtCNyJJEmVl35CX/xp2dsMYMvhXTEzcdB3W1Vpr0e7bQO03MTTkW+DwxPN0hA7i0Gfp\ntLY70d/L4kotsqTVknX8CEk/foOZlTWTlj6OZ1jfK0NdkrexKT6LlKJ6np4YRJhPE2+dfZGq1iqW\nRD7JeW0ozxTX8ZCHCW+FeGGqJ0ORKacxoQg9EwPs5gdj7NM9D01VV1fz66+/IpPJRBco4b8iErMg\ndBPNLVnk5Kylva0YjaYZa6v+3SspqxRw6n1af3qXyhRbjPuOx/21VVw42865zy+hUTsyeIoPA6f4\nIEkSuclJJP2wAwMjI25buATvfv2vLMM3tHWw5WAeP6WWsmiEL09OseeD9Hd5/1AKS/otRWU5lpeK\nqhltp+LA4GBcjY1QFjZSE1+EVqHGeooPJiF23W5ZH0ClUnHs2DFSUlIYN24cAwcOFCVQwn9FHP4S\nBB1TqZooKHyLqqrd+Pk9haPDRCorf8bVdQ5GRna6Dg8kCdJ/Qr1nDdXnrGkt18Nx5VqK9QM5E1eE\nd7g9/cZ7cilTTsgwFypzz3P8+69AguHz7sVvwOArCVSp1vDliWLeO5zP5D4uLBrlyM6Cz4kpiOGe\n0HsIcZ/LK4V1mOjpsS7Qnf5WZnSUt9CUUISqug2rid6YRf5ei9zdFBUVsXv3bhwdHYmOjsbKyuqv\nnyTcEsSpbEHoASRJS0XFTvILNuPoMAE/v6e7RyL+o5KTSPEv0pTRQlWyDMs7ptM0ZgHJ8aXYOJsx\nbGYADh4WSJJE8YVzJH3/FR3t7YyYt4CAwVHIfpspSpJEzPkKXkvIItjZkqcm+ZBU8wtfXPyCKT5T\niA5+kC1l7aQ1t7HS341pjjZo5Aoa9xWjzGvAapwn5kNdkRl0z5lne3s7+/btIzc3l+joaEJDQ//6\nScItRZzKFoRurqnpPNk5awGI6PchVlZ9/+IZXUxeAPvX0JGRQkWGDxq1NQarV5J4VoN0tIqxC0Lw\nDOn8ElF6MZ2jOz6jobKcEfPvo+9tk9DT078y1OkiORv2ZKLRSmycFU6VNpHHE18g0jGS9yd/yU65\nEfdm1PCIhxNbQr0xalPT8Gs+7Wk1WAx3w3ZmAHrG3fOjSpIkMjIyiI+PJzQ0lOXLl2Ni0s0O6Qk9\nTvf8bReEXqqjQ05+wRvU1h7A3/9ZXF1mda/uT+31cHQz0pkd1DWNQH7YCoMF93BR6oP8WBtR0/0I\nHOSMTE9GeU4Wx7//isaqCpz9AqnIzaKjre1KUi6oaWFTfBbpZU08OykIa/scNp99BFsTW94Y80/S\n1e7cfbGC8fZWHBocgqMko/lACfUnKzAb4Izz0wPRt+h+tciXNTQ0EBsbS319PfPmzcPLy0vXIQm9\nhEjMgtAFJElDWdm3FBS+hYvzNKKG7sXQsBvtP6o7IOVjOLqZNtORVCaGoPKw59LCpyjJb2PAZDum\nLu2HvqEeVYX5JH3/FTXFRUTNuovwsRNQtrXi4h9I+NgJ1LUoeftALjHnK3hktB8PTdBny7kVNF1q\n4ulBTyMzi+TpvHKsDOR81c+PviYmtJwop/JIKSYhdjg91h8D2+4769RqtSQnJ3PkyBGioqKYN28e\nBgbio1S4ccQesyDcZA2NZ8jOXoOBgQVBQauxtAjRdUi/kyTIioF9q9CYeVOd4039qYvUTPs7ueUm\nhI90Y8Bkb4zNDKktKSLphx2U52YxZPpc+o2fjIHR7zNahUrDx4mFfHSsgOmR7swcYsTnWe9xvuY8\nyyOX08d1MhsKK7nYomCVvxvRdla0n62maX8Jhu4WWE/2xtC5+9Ui/1FlZSW7d+/GwMCAO++8EwcH\nB12HJPQQ4vCXIHQDSmUNefmbqK8/QYD/8zg739m9ynvKzkDCS0jtDTSbz6Lik1iqh9xNLiF493Fg\nyDQ/LO1MkJeXceLHHZSkpzH4zllETIrG0Pj3Ga1WK/HVqWI2J2QzxNeO5ROc2XPpCxKKEngg/AHu\nDLybbaUN/FAp51FPJx5yd4Cs+s5aZAtDrKf4YuzdjVYPrkOlUnHkyBFSU1MZP348/fv3FyVQwn9F\nHP4SBB3SalWUln1FUdE23FznEDU0AQMDC12H9buGS3BgLRQeQ9X3b1TsTKdEXkHB0NXYetkw7beT\n1o3VlcRv+5aC1GQG3j6DiQ8vx8jU7KqhThbUsWFPJnUtSpo6WtFan+axY/FM85/Gz9N/JUauYXxK\nIVMcrDkyJATLS600br8Aai02d/hhHGTbvb6sXEdBQQG7d+/Gzc2NRx99FEtLS12HJPRyIjELwg0k\nrz9BTs5ajI2cGTjgW8zN/XUd0u8UTZD4Jpz5DGngQ8itB5P72mEK+y1A39OBcXMC8Qyxo6m2hn0f\nfkbOyeNETr6DxW9/gIn51V8simpb2RiX2Xmwa7I/ZdoEPsn4CDOL4Xw34TtyOyyZfaEce0MDvo3w\nI6hJS+OXWdTXKbCe5I1pP8duW4t8WVtbGwkJCRQVFREdHU1wcLCuQxJuESIxC8INoFBUkJu3kaam\ncwQGrsDRYVL3mQlq1JD6GRzeBIETaR/7GbmbvybbxpO2QY8ybHYQgYOcaW2s5+Cn28lMPEzf8ZNZ\n/NZ2TC2vXmJubFPxzsFcdqaW8vAoX6ZGVbD9/FL09fRRSe14OQzh+QIleW2NrPZ3YzxGNO8upraw\nCavbPDEf7NJta5EvkySJCxcusHfvXsLDw1m2bBnGxsa6Dku4hYg9ZkH4H2i1SkpKPqXk0kd4uC/A\n2/sR9PW7SSs/SYLcvbB3JVg6ox31EiVfH+PsBYk6l/4MmhZE3zEeKNubOf3rT6Qf2kf4mNsYPG0O\n5ja2Vw2l0mj56mQxWw7mMTncmRH9avn04jaM9I14csCTGBp7szQjlwbJkid9XHnAyhLloVLaL9Ri\nMcodixHu6Bnp/0mg3Ud9fT0xMTG0tLRw55134uHhoeuQhF5CHP4ShC5QV3eE7Jx1mJsHEBS4AlPT\nblTHWnkBElZAcwVMfJm6QiNOfZxIqcMQwkd7MGh6MJJWSUrMz6TtiyV4+GiGzpyLpd3Vp4wlSWLf\nxSpejcvC086MOcPV/FT0AXKFnCf6P8FIj7F8US5nY0EFbVotT7k7srSgg9bkSswGOWM5xhN98+7f\nTUmj0XDq1CmOHTvG8OHDGT58OPr63f+LhNBziMQsCDdRe/slcnLX09qaS1DgShwcxuk6pN81VcDB\n9Z0z5THPoXCbSvKrP5Gt9MMzyIoRDw7FyERLatwuUuN2EzAoimGz52PleG3no/SyRtbvuYi8tYPF\n40xJkn9FpjyTZRHLuMPvDg7I21iXX463qRGPuzlyIr2SySfrcAtywHKCFwbWPWP5t7y8nN27d2Ni\nYsIdd9yBvb29rkMSeiGRmAXhJtBoFBQXb6e07Eu8PBfj5fUgenrdJPl0tMLxdyB5Owx4AO3wJzj/\n0WFSz2mwtjNk9PJR2LiZczYhhpSYn/GNGEDUnLuxdbm2e1VVk4LXE7I5klPD4jE2XJJ+5nh5Iov7\nLGZ+yHyy2zSszitDrtKwyteVoQVtNO0rRs/cENtZgd2+9Omyjo4ODh8+TFpaGhMnTiQiIqL7nAsQ\neh1RLiUIN5AkSdTW7iMndwNWVv26V49krQbO7YBDG8B7BCw5QmFqE0lP7EUr02PsvaF4jQ4mbV8c\nP236EffQPty1+lXsPTyvGaqtQ80HRwv4PKmImYOsmX7bab4u3sNdwXcRMzOGFsmYv+dUcEjezLM+\nLsys09L2eS7t1kaY9nWk9UQ5HUVNPSIx5+TkEBMTg5mZGQ888IDolSx0KyIxC8K/0dZWSE7OOtoV\n5YSGvIKd3Qhdh/S7/EOw9yUwsoC7vqJW5cfR9Ueol2sZEGlMn0emknH0IB8/sRlnv0Bm/WMtTj5+\n1wyj1UrsPFvG5oRsBviYMn9SFruLvifaPppfpv+CqaEtWy9V82lpEfe52XPQ0RXtzyW0S2Az3R/j\nABu0bWoMbIwxG+Ssgx/Ef66pqYn4+HgqKirw9/fn7Nmz5ObmisQsdCsiMQvCdajVrRQVb6O8/Dt8\nvB/Fw+N+9PS6ySGm6izYtxJqc2HiWlpcJ5P08SmKs48TZFzKlHWzyM/L4LNnl2Hn7sn0Z1bgEhB0\n3aFO5NexIfYiBvoaZowtIP7S11ipovjm9m9ws/Dg+0o5mwqyGGZjzh4PdywPlKGpV2A1yQfTvg5X\napH1zQ2xHNN9TzBrtVpOnz7NkSNHGDhwIDNnzqSjowMHBwciIyN1HZ4gXEXsMQvCH0iSRHX1HnLz\nNmJrG0WA//MYG3eT2VRLDRx+BS7+CqOepqPPIlL2FJJ+5BLudSkMXjyMOnM9kn7cgaW9IyPmLcA9\nJOy6QxXWtrIxNpOMigYmDynjeN0OAmwDeLz/4wTbBZNY38yavHJM9fRY6WCHf2I1yqImrMZ7YT7Y\nGZl+965F/qOKioqr7rd2dHTUdUjCLUjsMQvC/0NLSzbZOWtRq5voE/42Njb/0d/Qzadqh5PbIGkL\nRMxHs/QU6SntpKxIwrYqjQl9ZHTMH0bsrz9hbG7BxIcfw6tPv+sO1dDWwdsHcvn5bCmTB8txtPqe\n3HYLXhn1CgOdB5LXpuD+8wVktSp40c2R0WfqUezJwXCUB7Zzg3pELfJlSqWSQ4cOceHCBcaPH09k\nZKS431roEcSMWbjlqdXNFBS+TWXlLvx8n8DNbT56et3gO6tWC+k/woF14BaJNH4NeUWWnPwxG+O6\nIoIaEzGaP5GUk0fR0zdgxF0L8IkYcN2TxR1qLV+eLGbboTyGhDZQb/ILSk0bTwx4gjEeY5CrNLxR\nVMkv1fUsd3VgXm47quQqzAa5YDXWAz2zbrKM/x/KzMwkLi4OX19fJk2ahLl59+5aJfR+YsYsCP8B\nSdJSWfkzefmv42A/jqih8RgZdZMa1uIkSHgRkMGsDyhThpL0YS4dVTn4p3+N5ZR+pNWZoz1xhOHz\nFuA/aOh1E7IkSey9WMXG2EycHOT0GZhAYXsJy0OXE+0bjRoZ71+q4d2SKqY7WBOrtsJoRxH6ofbY\nPjGgx9QiX9bQ0EBcXBy1tbXMnDkTX19fXYckCP+1G5aYZTKZPpAClEmSdMeNGlcQboam5nRystcg\nSRr69duOtVWErkPqVJcPcS9AaTJMWEOdyxxO7iqgtvAcfkUxmFrXkzPIAWVZIcPn3UvQ0BHI/mR5\nNr2skZdjLlKrqMAv7BgFLWd52Pdh5gbNxVDPkJiaRtbnlxNkZsIOAxucd5Zj5GmJ1SMRGDqZXXfM\n7uqPN3dFRUUxd+5cDAzEvEPomW7kb+4TQCbQ/YsYhVuWSlVPfsGb1NTsxd/vGVxd5yCTdYN9xzY5\nHH0d0r4F9wG0tspIPmxJQcVZAsnE7vyPFIX706rVZ/jtMwgZMRo9vevv91Y2/nZBSH4+fcJPo2w9\nxmCPe3k3bD3mhuakNrWyJq+YFrWGl40s6bevCn0rI6zvC8PIs+e1NCwtLSUmJgZTU1MeeughcXOX\n0OPdkMQsk8k8gNuBDcDTN2JMQbiRJElDWfl3FBS8hbNzNFFD92JoaK3rsEDdAac/gmNvQNh0Oh48\nQfLeatLlVfibKAg9t55iH0eaA90ZNm0WYaNvQ/9PZoKtSjXbjxbw+clMwkNTMfY5QKjLnbzZ71fs\nTOwoVXTw99xijtc384y5NROSa9HXtmE9zR/jQJsed+uVQqHgwIEDZGZmMmnSJPr27dvj3oMgXM+N\nmjG/BTwH9Lyv20Kv19iYSnbOGvT0TOkf+TmWlqG6Dqmz81NWDOxbBfYBaO+L4WKuFadfy8PEWItK\nKafo/G40vg5Ezb2HPrdNwsDw+gewNFqJn1JL2bw3HXevs1gGxOPnMprNkd/jZuFGi1rDxoIKviir\n5X4rK37N1mJUV9nZF7lv9++L/K8kSSIjI4OEhAQCAwNZtmwZZmY9a+ldEP6d/zkxy2SyO4BqSZLO\nyGSysf/mcUuAJQBeXt2oC4/Qa3V01JKTu57a2kME+D+Hu/s93WNGVZbaeWNXewPc/gbFigiSPszD\nxKyNCPsLpB/9GbWZMd5+wYx7eQOGRn9+ACspr5aX96SjMk3G1C8eT6c+vN7/EwJsA1BrJb4sr+X1\nwkpGm5nxY5k+tkcrsRr/W1/kHlSLfJlcLic2Npampibmzp0rPkuEXulGzJhHANNkMlk0YAJYyWSy\nryRJWvDHB0mS9AHwAXSWS92A1xWE65IkDWVl31JQ+BbmZv5oNC1oNK26T8qNpZ2lTwVHYNyL1DnN\n4PjPhTTX5RIa0kr+zrdJ0pNwjuiDNj8H6wGRf5qU82taeCU2k/SGRMyd9+Fl48STA94k0qnzFqvD\n8ibW5JVjI9Nja50B/geqOvsizwruUbXIl6nVak6cOEFSUhIjRoxg2LBhoi2j0Gvd0Drm32bMz/7V\nqWxRxyzcLE1N58nKXoWenjEhweswMnKkouJHXF3nYGRkp5uglM1w/O3OveTBD9HadxnJ8VUUnq8l\nfLg5lQfep7iylD59BzD82RfQajRkHN5P+NgJmFldvQ9e3/rbBSFZh3H0PIC1uR5PDXySEW4jkMlk\nZLW2szavnKI2Jc82GxB1sg7zHtQX+XqKi4uJiYnB2tqa22+/HVtbW12HJAj/NVHHLNxyVKpG8gve\noKZmLwH+f8fFZdaVGbK39xLdBKXVwNkv4dBG8BuLavFRziVrSHs1Hf8BlrjaHOLUjlP4W9mx6PWt\nWP6h5nbwtNlXDdWh1vLFiSK2Hj+MnecBXPzkPDHgMab4TkFPpkdNh4rXCyuJqW5gqcaYVxMbsQyx\nx+rxARjY9Kxa5Mva2trYv38/ubm5TJkyhbCwMN2veghCF7ihiVmSpMPA4Rs5piD8O5IkUVm5k7z8\n13B0nEzU0ITucdo67wDsXQmmNkjzd5B9yY1Tbxbg4GmIt3866TEJuLcouOuRx3C+488XmCRJIiGj\nkvV7j6Jnl4ClTyFLIpcyK3AWhvqGKDRaPiytYltJNTMwZueJNhxc9bFe0vNqkS+TJInz58+zd+9e\nwsPDWb58OSYmJroOSxC6jJgxCz1WS0s2Wdmr0GqVRPT7ECur698P3aWqszoPdsnzYeLLlMqGc/zz\nPGSyfFx9c8lJ3IOLvIno/kPwef4F9C0s/nSo86UNrI45Qbner8icz/Ng34XcG7oFM0MzJEnil6p6\n1ueXEybp81maEj8jCav5oRh79dyrBGpra9mzZw/t7e3cfffdeHh0345VgnCziMQs9DhqdQuFhe9Q\nUfkzfr5P4u4+n86L53Toj52fRj9LvedHJO0qofbSeRw9iihKTUAvU8voegUB6zZhNqD/nw6VWdHI\n0z+cpIJYjOxOMy94Ng/13YiNiQ0AKY2trM4rQ9muZm1OB4OaJayn9sxa5MvUajWJiYmcOnWK0aNH\nM2TIEHG4S7hlicQs9BiSJFFdE0du7gbsbIcTNTQOIyMH3QalUvzW+eldiJhP+8ITnD7YQM4PZ3Hy\nKKat7gDtCguG5lzC6667sV/yMHpGRtcdqq1DzZZDF/ks4xNkNkcJtBzG+9E7cTF3AaC4XcmGggqS\n5c08Vq5lSkkHtj20FvmPCgsLiYmJwdHRkaVLl2Jt3Q22IgRBh0RiFnqEtrZCsrPXoOyoJjz8LWxt\nBus2IEmC9J9g/1pw7Yf6gX2cP29I6qaL2DgUo2k7hKrBmWFNHdg0N+L66WcYBwRcdyitVuLH1EI2\nJX0O1gfx8bLjUquKif79cTF3oUmt4a2iKnaU17KgQcbzGa04j/XCfLYLMoOeV4t8WWtrKwkJCRQV\nFREdHU1ISIiuQxKEbkEkZqFb02gUFBVvo6xsBz7ej+LhcT96ejou+yk51dn5SatGmvEeeXWBJL2T\ni6FhPtr2o0hqF0Z5BmCwOxaHx/6G7fz5f9poIrmwmucTPqPBeA9hvkG8NPwDXMxd+CXvF+7wn86n\nZbW8UVDB6FYZ351rxXeIOxbPhPXIWuTLtFot586dY//+/URERLB8+XKMjXvmyXFBuBlEYha6rdra\ng2TnrMPKqi9DhsRgYuyi24DkhbB/NZSegfGrqDSfxLHvcmmpi0PdnoSxvQ23Tbod2YefYOTlhcvP\nOzF0uX7MJfIWno39kizlD3g7uLB55D8Z6DIA6Fyy93CZxay0cuxbNbx7rpX+IU5YPhbcY2uRL6uu\nriYmJga1Ws19992Hq6urrkMShG5HJGah22lvLyMndx2trXmEBL+Mvf0oHQfUAMc2w9mvYNhyGke+\nRdLuMkozdoH2FKaWxoxe8ABmCQdoeeMtnFa8iOXkydc9iNWiUPHS3u85UPU5DubmvD1hHWO9Rlx5\nbHpzGytzyshuauPpLCUzHa2xfjASA5ueXS6kUqk4evQoZ86cYezYsQwaNAi9P1lFEIRbnUjMQreh\n1XZQUvIxJZc+xtNjIX37vIOeng6XODUqSPkUjr4GwdEoFyVx+kgL6d/tQY9TGJlIjJh/P85NbVS9\n8BLSyBH4xexG/zqHl7Raic3HYvg6ZzumxhpWj3ya2SG/J+9yRQevFlRwsLqRPrUq5Pb6tA5zxj7S\nu6vf9Q2Xl5fHnj17cHNzY+nSpVhZ9dxyLkHoCiIxC92CXH6c7Jw1mJn6MHjQz5iaeuouGEmC7LjO\nzk/WHmju/YWMbGtOvnwESXMCAwMFI++6F/+AEKo2vkp15kXcXn0V86ih1x3um7SjvJnyNhq9epZE\nPsqjg2aj91sP6Ga1hneLq/jiUi2zKtTsatFH5mzFt9l1zAjpuSetAZqbm4mPj6esrIzbb7+dwMBA\nXYckCD2CSMyCTimVVeTmvkJj01mCAlfh6DhBtwFVpEHCCmitQZq8kcK2CI6+lUh74zH09BoYcde9\nhI4cS/OuXRT+fRY2s2fj9upG9K5zM9XhwnOsPvYG9aoipvs8wMqx92Ok31kqpdJKfFVRxxt55QyX\na/muQkvweB+Mg2zRtql5LMUUs0HOXf3ubwitVsuZM2c4dOgQAwYMYPr06Rj9SYmYIAjXEolZ0Amt\nVk1p2ZcUFW3F3W0+oaGvoq9vqruAmsrh4HrI2w9jnqfaYRaHvjpJbfEmZFQzfN7d9L1tIpqyckof\nfAhtSwteH3+ESei1vZ0zavJ4/sBrFLemM8x+Hq9N3o6Naef1mJIkkVDbxLrsUhyb1GzJ72DIKG9M\np/9ei6xvbojlmJ5541VlZSW7d+9GT0+PBx54AGfnnvnlQhB0SSRmocs1NJ4hO3s1hoY2DBzwHebm\n/roLpqMVjr8Dydth4EKa703iyI/pFKa+ApQxbNZcIiZHYyDTo+7Tz5B//An2jzyC3X0LkBlc/edT\n0lTKiwffIE1+ggDjaH6dsQlf+987IaU2tbI2s5S6RgVP5SqZ0t8di0dde3Qt8mVKpZLDhw+TlpbG\n+PHj6d+/vzjcJQj/TyIxC12mo0NOXv5ryOuOEhD4D5yd7tDdFZJaDaR9Awc3gPdwOhYeJml/Nee/\nfgNJU8DgO2cy6M51GJmY0p6ewaWVKzGws8Pnxx8w+pf7m2vaang58R2OlO3DRjOG7bf9wHC/3/fI\ni9uVvJJTxonaZh7JU3J3gDM2D3mgZ9xza5EvkySJrKwsYmNjMTc3Z+HChTg5Oek6LEHo0URiFm46\nSdJSXv4d+QVv4uIynaioBAwMLHUXUMER2LsCDM3Qzv2CsxmmnFjxMWpFNhEToxk2ZwUm5hZo29qo\n2vQajb/+ivNzf8dq2rSrvkg0KBp4K+UDduXvRK9lMC9EfcL8AaFXHtOgUvPP/Aq+K5czv6SDeAc7\nnBeE9fha5MvkcjmxsbE0NDQQGBhIamoqubm5IjELwv9IJGbhpmpqTic7ezUymR79I7/A0vLaPdku\nU5vb2Yqx+iJMXEdOaz8OvrqD9oY0QkaOZ8yCZzGz6ix1ajl+nMrVazDt3x+/3b9iYGd3ZZiWjhY+\nOv8ZX13cQUdTH+4Nfosnxg7GxLBzBqzUavm0pIZ3CisZW6Fil5El/tODMbDt2bXIl6lUKhITE0lO\nTmbEiBFERUWhVCqxt7cnMjJS1+EJQo8nkySpy1900KBBUkpKSpe/rtB1VKomCgrfpLo6Dn+/Z3F1\nnY1MpqM9x9Y6OPJq593WI5+i3G4GCR9+S315Mr79hzPhofuxtLMHQF1fT/Wrm2g7fRqXNauxxqLl\nGAAAIABJREFUGD36yjAKtYIdmd+wPe0TFE0BjLS/m9VTR+Nk1ZlwJUni16oG1meV4iNX8YzCiIHj\nfTF0NtfJ274ZcnNziY2NxcXFhcmTJ2NjY6PrkAShR5DJZGckSRr0nzxWzJiFG0qSJCqrdpGXtwkH\nh9uIGhqPoaHtXz/xZlAr4dibkPQO9JlD/dwDxH0aQ2Xu07gGDWDRm+9i6+pyJe6mmD1UbdqE9e3R\n+O3+FT3zzoSq0qj4Kfcntp7djqLFAzftk6yfNoG+Hr9fJHKyvpk16ZdQNClZVSdj0pgAjL17z0Ua\nDQ0NxMfHU1VVRXR0tKhJFoSbSCRm4YZpackhO2cNGnUL/fq+h7W1jpY1JQkyfob9a8DAhDaFloST\n1hR++zz2HqHcs+ENXPy8rjxcVVZGxdq1qCur8Ny6BdOICADUWjUxBTG8m7qNjnYH1LULWTtpElP7\nuFzZR85vU7DufAlpTW38rULL3UO8MYu267F9kf+VWq3m5MmTHD9+nKFDhzJ79mwMDXvHHrkgdFci\nMQv/M7W6laKiLZRX/Iiv7+N4uN+DTKajE8eXTnd2flIrUEX/k9hdWeTl7sfcppVZ/1iPT7+gKw+V\nNBrqv/6a2m3vYbdwIfYPLkZmaIhW0rKveB/vpm6hTWGK/NIsHhk6kUX3+FzZR67tULM54xK/1DVy\nX7maN/t4YjfBqUf3Rf5XhYWF7NmzBxsbGx5++GHs/rDPLgjCzSMSs/D/JkkSNTUJ5OSux9Z2KEOH\nxmFs5KCbYOqLOnsjl5xEO24FSTmWpKz7BEnSB0mFS0D4VUlZkZ1DxcqV6BkZ4b1jB8Z+vkiSxNHS\no7yT+g6NbRrqSicz0WcUzywLxsmycx+5XaNle04575fXMqVSTYK3M173uPeKWuTLmpub2bt3LyUl\nJUyZMoWQkJBeswIgCD2BSMzC/0tbWxE5OWtRKCsID3sDW9vr3xN90yka4dgbkPoF0pClpFnMI/Hd\n79FoTRg6aylBQ0M49s0uRt87AwCtUknte+/R8N33OD71JDZz5iDT0+N05WneSX2HqpYGFNUTcTEc\nxFv3hBPu1rmPrJUkvi+qYVNBBaFyNd/Z2tJ3jhd6xr3nT0ij0XD69GmOHj3KgAEDWL58ubhKUxB0\noPd8qghdQqNRUlz8PqVlX+LttQRPz0Xo6elgz1GjgjOfwZHXkAInkTv0fQ5++zOKljxCR81h3AOT\nMTLp/PWe8exDALSdPk3FylUYBwbi+8svGDo7caHmAu+cfYeixkuYt0XTXhXOiuhwJoc7X5klHqlq\nYG3GJfSaVWw2MGfsVF/0LXpXwrp06RIxMTGYmpqyaNEiHB0ddR2SINyyRGIW/iOXb+2qr0/C0rIv\nQwb/iomJW9cHIkmQE99Zj2ztTsnQ19m/8xBNtd/iHjaVyY9Mw8r+6ju3NU1NVG9+g5YjR3B+aQVW\nEyeSU5/DloPryai9iKfeNGoyZzFnTBAL7/XB2KBzHzmrsY3VZ4vIb1PwdIcJc0cFYGivw/u8b4LW\n1lb2799PXl4ekyZNok+fPmLZWhB0TCRm4S8plJWcO7eY1tZs3FznEhr6qm4Cudz5qaWayvAnOHAg\ng5p9P2LjOo55a2bhFnBtWVb9zz9TveEVLCZMwG/3r5RSz/qjz5FckUyE5UwacqYwNNyTzU8H4WDR\n2fu5sr2DjWcK2dvWxpJmfT4eFoiFmw5vKrsJtFotqampHDx4kH79+rF8+XJMrtMhSxCEricSs/Cn\nJEnDpdIvKCraiovLLJyd78DdbX7XB3K581PuPmr7LONIeROln8VhbDGMyUuXEzLM45rT0Krqaqpe\nXk9bSgralhY6vJx4Of1NDpYcZITTTPTLXqTG0oqvHgwj1LWz3rhFpWbL2RI+bWxkRqOMI/29cfLv\nfSeRy8vL2bNnD3p6etx///24uLjoOiRBEP5AJGbhupqazpOV/RL6+ha66wClbOm8HCT5AxoC55Oo\nv5iCb5PRNx7I4BmrGHx7IIb/0ghCkiQaf/qJ6jf/ic28uRg+s5Rjn77CR8Y/EKWdhXf7Wk6cgRW3\nhzEh1AmZTIZaK/FVeilvVNYxsEXL7kB3Aic49bol3fb2dg4ePMjFixeZMGECERERogOUIHRD4kpO\n4SpqdTP5BW9QXR1HgP8LuLjM6PoEpdXAuR1waAPNTsM42RhM5ulzGJpG4hM5gZHz+mBpd+2ya0dx\nMRWrVqNtbcV85d/5Wn2cH3J+wNfKH2flAg5n6LFsrD/3D/PByEAPSZLYm1/Dy/nlWCm0rHR1JGrQ\ntbPvnk6SJNLS0ti/fz/BwcGMHz8eMzMzXYclCLcUcSWn8F+TJInq6lhyczdgbz+GqKEJGBrq4B7k\n/EOw9yXasCDZ9H4uHEjDxFKLU8CjjLknEld/62ueIqnVyD//nLoPP8J88X3s7N/Bd5lPM8l7MgHG\nkzhb+xPBhiHse+pZ7H/bRz5X2sCajBIq1WpesLRh2m3e6Bn2/DaM/6qqqoo9e/agUqm4++67cXd3\n13VIgiD8BZGYBdrbS8jOXo1CWUmfPu9gY/Mffam7sWqyYe9KlJW5pJjcydkzOVjYSZg7LGL4nAiC\nh7hcdyaryMyk4qWVSBZmJK6ZxqcN3zBeNZ5nwt9j6z45HdomFNo2Rg6Kxt7CmJK6VjacKSRRUvE3\nfXMWj/LF2Kz3XTGpVCo5fPgwaWlpjBs3joEDB4pla0HoIURivoVptR2UlHxEyaVP8PZ6GE/PxV1f\nk9xSA4c3okrfxVmz6aRkGmDpaICR5T2Eju5D/0leV+qRr4pdqaR26zbqf/yBrLsG84ZTKqMtvNgU\n+hEfHWricE0tK24PY4CXDT+eCWNymDOrDmTxnaadu7XGHI8Kwcamd5U+QefKR0ZGBnv37sXPz49l\ny5ZhYWGh67AEQfgviMR8i6qvP0VW9ipMTT0ZPOgXTE09ujYAlQJObkOTuIULJuM5WTgMK0dLjK3H\n4OTvz7CZ/tfUI1/Wdvo0ZStXUulizGuL9egTbMbW4E/ZldzB3w6VsHSMH+8tGICxgT4dHRq0Monb\nU3MZpTFgX39/vFx7T9enP6qtrSU2NpaWlhZmz56Nt7e3rkMSBOH/QSTmW0xHh5y8vFeR1x8nKHAV\njo6TuvZwlyRB+k9o960lUxVC0qWRmNs7Yuk8FAMTN6YuDMQt4Pp725rmZspf24T8wF4+maSH0bhR\nvNlvKadzDFn0QQ4TQp1IeHI0jpbGaDVafjpVxMY6OTIZbPFyZVy4a9e9zy7U0dHBsWPHOHPmDKNG\njWLIkCHo6/e+/XJBuFWIxHyLkCQtFRU/kZf/Oi4u04kamoCBQRcvcZacRIp/kdwqGcerB2Bk5YiD\n/xgaq22JmuFP8NDr7yMDyPclcGnNSpJ9NeS/NJzlwx6jTm7P419cxNLYgM8WDaaPuzWSJHEkrZwN\nl6pQ6suI0jPkR2MNZ2uaGUfvS8xZWVnEx8fj4eHB0qVLsbLqnasBgnArEYn5FtDSkkN29iq0WiX9\nIz/F0jK8awOQFyDtW01RRiaJjWFIxja49Z1MSZYF/v4e3L7c+7r7yABtVRWkvfgYHZlZJN0fycx5\nLzEFL17Zk8n50lJejA4lum9nf+QLOTWszy4jx0jiWRd75g/wQN6kxO/cJe6L9Oza93yT1dfXExcX\nR11dHdOmTcPPz0/XIQmCcIOIOuZeTKNpp7BoC+Xl3+Pn+wTu7nd3bZ/k9no4upnSxF9IbI6kHXN8\nB02jKN0GV3+bzn1kh+vvI3doOjj6wRqsPtpFznAP+r+wEW+Hfmw7lMeO5BIeHOHLw6P9MDHUp+RS\nI5vOFXHQWMtSCyuWDPHB1KB3LuWq1WqOHz/OyZMnGT58OMOGDcPAQHy/FoTuTtQxC9TWHiI7Zy3W\nVhEMHbIHY2OnrntxdQekfExV3BYSm8KQdwwmfNwcyvMdqS7RY9KDgbgFXn8fWa1VE3/8c9SbtmCj\nNMDknQ3cM2w6O8+Wsfjzw4zwdyD+idG4WJsgr2llQ3Ih3xuqmGdlRtIQX2xNe1fXpz/Ky8sjNjYW\nR0dHlixZgq3ttXeDC4LQ84nE3MsolJXk5qynuSWDkOB12NuP7roXlyTI2kPdrnUkVTpT1tqPyOi7\nsJT7kX26iajpnoREuV53H1mj1RCbF0PG+68x6UgTBgvm0PexFaSWNTNz23FkMhnvLRjIAC9b2poU\nvB2fyXaZgrEmxuwfFIynde+9yaqxsZGEhATKy8uJjo4mKChI1yEJgnATicTcS0iShtLSLyks2oK7\n+z2EhW1GX78LuwWVn6Xx5xWcyO6goMWbAXfMw1G/H+lHqwgfZc69a8OuX48saUkoSmBn3D+Z/4uc\n2+28CN65gzobJ5788QKnCuQ8PzWY6RHuaDvUfH0glzeVzQQYGvJ9P3/6OPfew04ajYaTJ0+SmJjI\nkCFDmDlzJoaGve8yFEEQriYScy+g04YTjaW0xKzh5MksspuciJw6n7EeozgdW46zTwfz/jH4uvvI\nWknL/uL9fHBmK5MON/Hk6Vbcnn4e4+kzee9YIZ8mHeO+KG9emdkXM3099h4vYmNDPYbG+vwz3JvR\n3vZd9x51oKioiD179mBlZcVDDz2EvX3vfr+CIPzuf07MMpnME/gCcAYk4ANJkt7+X8cV/trVDSee\nx8VlZtfVJCubad//OsnxCaQ3uhA+7h7uGDyNlNgqSvNrmLgoDLfAa/dAJUni4KWDbDu3Db/iDlbv\nbsEmqA/Ou14ivlLDpn8eJdLTht1/G4mHjSlnUsp4payaS+Z6vBDoyqxgl17X9emPmpubiYuLIz8/\nnylTphAZGdmr368gCNe6ETNmNfCMJEmpMpnMEjgjk8n2SZJ08QaMLVzHtQ0n4jE07KKDQBo1Hac+\n4cwPn5Ba60RQ1CzmRN/HhSMNHPyyiKHT/AgZ5orev+wjS5LEsbJjbDm7BSOFmheTHbE6lYXzihUU\nhw/lqZ0ZtKs0vDkvgiG+duRlVPPwoSxOWOnxuK8ji/q5Y9SL73pWq9UkJyeTmJiIo6MjSqWStrY2\nkZQF4Rb0PydmSZIqgIrf/rtZJpNlAu6ASMw3gc4aTrTWoYpfSdrpDE6XWeDddzx3Pf0oRRfUxGzJ\nJ2ykG/euicLI9OpfKUmSSCpPYuu5rSg0Cp5WjMH5vV8wHxGG3jcv83JSBYc/P80zE4OYO8iT2sJ6\nnv8pjV3WEvd72vBmfy+sDHv3jkt+fj5xcXHY2NiwePFiTE1NOXfuHJGRkboOTRAEHbihdcwymcwH\nOAr0kSSp6c8eJ+qY/3u6bDihKT/P2beXc6LEHHcnc0Y9vZmGGjNO7MzHyduSYbMCsHa8eh9ZkiSS\nK5PZem4rjcpGlvvcR9iXJ1BcSMdh9Wq+UTnzwdF85g7y5G+3BYBcwfsnC/nEQsNUM3OeH+iDSy8u\nfYLOS0ISEhKoqqpiypQpBAUFiRmyIPRSOqljlslkFsBPwJPXS8oymWwJsATAy8vrRr3sLaG+Ppms\n7JVd3nBCaigj+4uXSEopQzJxoUPbjm3faI79IKdDUcP4B0JxD752CT2lMoWt57ZS017Do/2WMvyC\niprlb2A4fRoX732MxfsLCXKuZ+eyEbjJ9PgqIYd3jTvoa2fM7gEBBFr13tIn6Lzb+vjx4yQnJzNs\n2DBmz54tTlsLgnDFDZkxy2QyQyAGSJAk6c2/eryYMf9ndNVwQlI0U/z9yxw7eAaZuT2jFj2OgZUf\ncdu+B1kow2f3JWT4tfvI56rPseXcFsqay1gasZRJxv2pWfsy6tpalE+9wMs5EjXNSlbdGcYwFyv2\nHC3idakVKzNDVvf1Zqhj7y19gs5VhMzMTBISEvDw8GDSpElYW1vrOixBELpAl86YZZ2Z4mMg8z9J\nysJfu7rhxLSuazih1VC+520Sd8XQgiUjF/wNvzHTOH+olNOf56BW9WPInb6EjXS76mkXai6wNW0r\nhQ2FPBLxCHf4RNPyzQ9c2nYXpvfez6duUcQereWJCYHMj3Dj1PFLzEgvQW5pyEvB3kz1sOv1S7jV\n1dXExcXR2trKjBkz8PX11XVIgiB0UzdiKXsEcB9wQSaTnfvt/70oSVLsDRj7lqOThhOSRO3x7zm+\n42MqWw0ZPm0+4TMepORiPd++nIyNsxnTn+pPeV4DocN/79B0se4i285tI0uexZJ+S5g5bibagiLK\nFyxEMjAg5dnX2JypYJq3EfufGEVZWjUP7rlAmq0+z/Rx515/Zwz+pJtUb6FQKDh8+DDnz59n9OjR\nDB48WLRkFATh3xJNLLqJzoYTWykv/65LG040XTxK0sevU1ClZsi4kUQseIbWBi2JP+TSWNPOiDkB\n+PR1uOo52fJstp3bRnptOg/2fZDZQbMx1Mio2/4B9Tt2IJ+/mJdUfrjamrMqOhSj0hbezKsgwVGf\nh53tWRrmhnkvT05arZa0tDQOHDhAUFAQt912GxYWXdxmUxCEbkM0sehhausOk529pksbTrSVZnFq\n+1ou5jcQOSiUB9esQmZgwemYIjKTKhgw2ZupS/uib9BZO1yvqOejCx9R0lRCel06i/ssZtPoTZgY\nmNB29iylK1eicnZny92ryOgw4aXoECIkvc5uUI56zAy0JbGfFw5Gvf9XrqysjLi4OCRJ4u6778bd\n3V3XIQmC0IP0/k/JbkwXDSeUDVWc+WA1Z88VERrsysJ/bsfM0ZPsU5Wc+CUdrzA75q8agrm18ZXn\n5NXn8cKxF8iuz2aU+yj2zNyDmaEZ2tZWKl/dQGN8Asen3M8WrRePRgaw3tWWr1OKedJOIsrHgrhI\nL3zNuvDebh1pbW1l//795ObmMn78eCIiItDrxZeiCIJwc4ilbB1QKmvIyl5BQ0MKHh4L8PFedtMb\nTqjb20j7fD3Jx1Lxcbdk+JJ/YB0wgKrCJo5+lwPAqLsCcfH9/ZRwbn0u289vJ6UyhbnBczGQGTAv\neB62Jra0HDtGxeo1VPqF85LrbQzv78+TEe4cSinjLUs1rhbGrIrwpr+1+U19X92BRqPh9OnTHD16\nlH79+jF27FhMTHr/FxFBEP5zYim7G2tuziDt/BKUykq8PB/C3+/pm/p6WrWaiz9uISk2ASdrPeY8\n+QSOg6fS2qjkwOcXKbkoZ9gMf4KHulxpx5hTn8P7ae+TWpXKwvCFrBu+DjPDztpidX09Zaueo/5U\nCh8MmkdVUATvjQ6gPLOG+9OLUDoZsiHcj9scrXr9SWuAwsJC4uLiMDc3Z+HChTg5dWHfa0EQeiWR\nmLuIWt1KYeHbVFT+go/3crSSEjfXOTft9SRJIm/vtyR+/zWmeh3cvuAu3CcuRqOROLu3hNSEYkKH\nu151jWa2PJvt57dztvosC8MXsn7E+isJWSWXU73hFZqSkjgTFMUnE//OC5P7YFfVzrr0EnLsDXk+\n0JM5Hg7o3wIJubGxkb1791JaWsrkyZMJDQ29Jb6ICIJw84nE3AVqaw+RnbMaG+vBRA2Nw8jo5rbw\nKzl1gGOfb0XT1sTYqWPxmf0cMgMjitPrSPwhF2tHU2Y/NxAb586kmyXP4v2090mrSWNh+EI2jNyA\nqcHvV2yqysvJX7gYqaSYuMBRmC9YylatPu/kVnHE2ZDlwa585ueCiX7v309VqVScOHGCEydOMGTI\nEKZPn46RUe++OlQQhK4lEvNNpFRWk5P7Ms3N6YSEvIK93cib+npVWWkc+/A1GmuqGTEilOD71iIz\ns6Whqo3EHzNpqGpj5NzAK+VPmXWZvJ/2PhdqL7CozyI2jtp4VUKWtFrkX++g/J0t7PIYTEt4HwZN\nnM3ZiiZmuBtwdz8nkoLdsOnlTSagcwUiJyeH+Ph4nJ2dWbJkCba2XdTRSxCEW0rv/0TVAUnSUlb+\nLQUF/8Td7S7CQl+/qYe75JeKOf7hK5QXFBPVz4E+L36Ivr0PHQo1KTvzyDxeQf/JXkx9pLP86WLd\nRd5Pe5+M2gwW9Vl0pezpj5R5eeQ+9w9K6pX8fOezzIsI5wNFK7vsDBhvZ8mBcE88TG6NmWJtbS3x\n8fHU19dz++23ExAQoOuQBEHoxURivsFaWrLJyloBMhkD+n+FhUXwTXut5toaTnzyOnlp6Qzy02PK\n+nUY+gxB0kpknazg5M/5eIb+Xv6UUZfB++fe52LdRRb3Xcxro1+7JiFLHR0Ub3kP+Vdf833fqUxY\nOJ+ounaWmyposjJgESZsHOh/095Td6JUKjl69CipqamMHDmS+fPnY2Ag/mQEQbi5xKfMDaLRKCgs\n2tJ5c5ffU7i7zUcmuzl7ru3NTSR/vY30xET6Obey+O9PYBIxHWQyqoqaOPZdDpJWYsrSvrj4WpNR\nm8F7B94jU57Jg30eZPPYzRjrG18zbkNKKrl//wfZelbIlr3BAAML1hkosAg04S1vJ7Ly5dwX6XlT\n3lN3IkkSFy5cYN++ffj6+rJs2TIsLS11HZYgCLcIkZhvgDp5ItnZK7G07HNTb+7qULSTuvNLzsTF\nEGwt54EH52MxeinoG9DW1MGJX/Ipyagjaro/IVEupNels27/e+TU5/Bg3wd5Y+wb103ImpYWUlZt\nRDq0n/TJS3AJGchWOy0t1oa8GOrBFEdrZDIZ0Z4O14mqd6moqCAuLo6Ojg7mzp0rWpQKgtDlRGL+\nH3R01JKb+woNjSkEB63FwWHcTXkdjVrF+bhfOPXTDjxNarhn5hhso58HEys0ai3n93WWP4UM6yx/\nymq5yLKD68itz+Whvg/x1ri3MNK//n5w5q4EGja8TInnQKyWb2WfrYxcOz2eC/Jgrpv9LVH6BNDW\n1sbBgwfJzMxk3LhxDBgwQNzaJQiCTojE/P8gSRIVFT+Sl/86ri4ziBoaj76+2Q1/Ha1WQ9axQyR9\n/QF2UjWzRvvjNPtdsPYAuFL+ZOVgyqxnB1Cin8fjx/9GfkM+D/d9mLfHvf2nCbmutIrkv6/EsvgS\nzfPWsM/DhhNOhjzm68LnXo63ROkTdDabOHPmDIcPHyYsLIzly5djZnbj/y0FQRD+UyIx/5daWwvI\nyn4JjabtprVllCSJgjPJJH6xDaP2CqaEGeEx/21wjQCgobqN4z/kUv9b+VODcykvpD1NYWMhD/V9\n6P/au/OwqM9z/+Pvh10UAUEFEURwBVdwi6JRDJqYxGg022kWd5NUc9L2nJOeZk/7a9OmbfY0tVlN\nTEyMRmNqCCC4sGjcBRdk3xdRkB1mmOf3Bx6btlGJjAwzc7+ui+tymJnv3HOLfvjO91l4bdZrlw1k\ng7GNb19bj+8nH+A8azmb541kR4ALSwN8eTnUDw8n29716fsKCwvZsWMHLi4uPPDAA/j5+Vm6JCGE\nkGDuKJOphfz8tyku+YjBwWsYOPCB67ItY/GpDPZ+8BatVYVEBdUQcu9TqGFzQSlam40c+iafk8ll\njJ8ThN/CNn6b8SsKMgtYMWYFC0IX4OzofNljp6WeoOz53+DXN5wdj/yBz4NdWdDfm+RhA+jrcvnn\n2Zq6ujri4+PJy8tjzpw5jBo1SlbtEkJ0GxLMHVBdvZ/TmU/h7h7CpIlf4eY2wOyvUZmfS/JH6ziX\nd4pp/YoZsfpRHCIfAkcntElzZn8ZaV/mMHBkH8IeceOt3F9TnFbMytErmR86/4qBnF9Zyze/fpPJ\nRRVk3bGGp4f1ZEYfD74dOZBBPf59MJitMhqN7N+/n+TkZCIjI1mzZg2urvbz/oUQ1kGC+QoMhhqy\nsl/k/Pm9DB/2LH37zjH7a9SUl5Gy8X2Kjh5gsk8B8+9bgNOMj8G1fXrO96c/DVrsxIbzf6b4WDGr\nxqzi9tDbcXa4fCDXtxhZvyGRsO1xEHULK27rwwivnnweHkh4rx6XfZ4tys7O5ptvvqFPnz6sWLEC\nH5/ruyyqEEJcKwnmH6C1prxiG9nZv6Nfv3lMmRyLk5N557HWV59n3xefkJmcSGSfEmJuHY/LnDfA\nMwCAxtpW9m3NoeDEOfrPdGCzepfSwlJWjVnFbaG3XTGQTSbN1v251L69id6h4Ty17F5693HnzfAg\nbvDqZdb30d2VlJSwdetWWltbmTdvHsOHX78FX4QQwhwkmP9FY2MBmZnP0Go4x5gx6/DsPdasx29p\nbCD1k3c5nhhPuG8dS6M8cL/tb+A/BoA2o4n0XcUcii3AazSkRH1EaVP7GfKtIbdeMZABjhRW8+1f\n4xiqHPl0/iwa+/TgqVFBzPX1tKvrqC0tLSQnJ5OWlobRaCQ6OlpCWQhhFSSYLzKZWiksfJfConcZ\nNGg1gQOX4uBgvvYYDQaOxe3guy2f4KHPY2xzxdM/EPcV6+FiYBacOEfy51mYPFo4MHkzRY45rBrZ\nHshOV6mloraZDz47zODcMg6NDuKzvi48ETbIruYiQ/v0p2PHjpGYmMjgwYNZuXIl2dnZjBs3ztKl\nCSFEh0gwAzUXDnH69FO4ufkzccJWevQYaLZja5OJ0ym7Sf70fXyd67grOAf3acs4kZFP+N2Pg1KX\npj+VlZwnfWgCOZ7HWD12NbcM/vNVA7nZ0MYn8VmQkk3m8D58eGMQjwX35aOhQXYzF/n/FBQUEBsb\ni6OjI/fccw8DB7b/Pfbv39/ClQkhRMfZdTAbDLXk5L7E2bMJDBv6JP363WrWj3vzjx1mz8fv4NR4\nllv6nGTgnKUwZQO4uDMxGlqbjaR+mc3xPYXkDT7IqchUVo5bzp8GP3/VQNZas/NQCZlfn+ZMkDvf\nRPXjQTd4dXqEXc1FBqipqSE+Pp6ioiJuuukmRo8ebVcf2wshbItdBrPWmsqz35B15jf4+kYzZXIs\nzs6eZjt+RW42ez5+l7qSbKK8Mxk6by5q5l+gZ/ta0411Lez9LIv8U5WUeWeTMSmRJZPv57fBv8DR\n4eqheqawhqTPTlDgqdg8uTfzairZO3UG/T17m+09WIOWlhZSUlI4cOAAkyZN4o477sDFxT62ohRC\n2C67C+amphIyzzxLc3Mxo0a9hpfXBLMdu6ainJSN6yk6/h03+BYxatZwHGO+BJ9/bJNY9fV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/JKbCZ/r27kufnhzBzeD4C2mhoq/vCSXUyBamlpISUlhQMHDhAZGcnatWtlowkhhOhGrD6Ye/Ry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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4162aac4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "D=10\n",
    "xs=np.linspace(0,1,D)\n",
    "plt.figure(figsize=(8,6))\n",
    "for i in range(10):\n",
    "    ys=np.random.multivariate_normal(np.arange(xs.shape[0]),k(xs,xs))\n",
    "    plt.plot(xs,ys,'o-',lw=1,markersize=1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "提高维数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EnO9JS0cgKE3LTrHc2KMeFtv/VUnp8eOkDHsV+9mzYDYTPmQIwU/2QxkMHhyiapOiFkII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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f41644a6208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 100\n",
    "xs = np.linspace(-5, 5, n)\n",
    "K = k(xs, xs)\n",
    "mu = np.arange(xs.shape[0])\n",
    "plt.figure(figsize=(8,6))\n",
    "for i in range(5):\n",
    "    ys = np.random.multivariate_normal(mu, K)\n",
    "    plt.plot(xs, ys, linewidth=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 高斯过程预测"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "假设$0.03X^5+0.2x^4-0.1x^3-2.4x^2-2.5x+6$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f4160c3f5c0>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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cPj4tl/KaJl5fv4e5a3ezaMtelhfvY3nxPn4OpCbEMGvEQE4aOZDJuelMGJLa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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f41629c13c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# coefs[i] is the coefficient of x^i\n",
    "coefs = [6, -2.5, -2.4, -0.1, 0.2, 0.03]\n",
    "\n",
    "def f(x):\n",
    "    total = 0\n",
    "    for exp, coef in enumerate(coefs):\n",
    "        total += coef * (x ** exp)\n",
    "    return total\n",
    "\n",
    "xs = np.linspace(-5.0, 3.5, 100)\n",
    "ys = f(xs)\n",
    "\n",
    "fig=plt.figure(figsize=(8,5))\n",
    "plt.plot(xs,ys,lw=2)\n",
    "plt.ylabel(\"$f(x)$\")\n",
    "plt.xlabel(\"$x$\")\n",
    "plt.title(\"The hidden function f(x)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_obs=np.array([-4.,-1.5,0.,1.5,2.5,2.7])\n",
    "y_obs=f(x_obs)\n",
    "x_plot=np.linspace(-5,4,80)\n",
    "y_plot=f(x_plot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "#计算新的协方差矩阵\n",
    "K = k(x_obs, x_obs)\n",
    "K_s = k(x_obs, x_plot)\n",
    "K_ss = k(x_plot, x_plot)\n",
    "\n",
    "K_sTKinv = np.matmul(K_s.T, np.linalg.pinv(K))\n",
    "\n",
    "mu_s = m(x_plot) + np.matmul(K_sTKinv, y_obs - m(x_obs))\n",
    "Sigma_s = K_ss - np.matmul(K_sTKinv, K_s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "高斯过程中，每个随机变量的方差中会包含不确定性，而矩阵中第i个随机变量的协方差是Σ∗ii，也就是矩阵Σ∗的一个对角元素，所以在这里，我们得到样本的标准差为±2。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f41609ccc88>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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P57Of/Sx5eXksXLiQe+65h/Lycjo6OvjCF75AT08P73//+1m+fDkbN27k9ttvB+Cuu+6i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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f41644b4630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig=plt.figure(figsize=(10,5))\n",
    "plt.plot(x_plot,y_plot,'--',label=\"True f(x)\")\n",
    "plt.scatter(x_obs,y_obs,marker='x',c='red',label=\"observe\")\n",
    "stds = np.sqrt(Sigma_s.diagonal())\n",
    "err_xs = np.concatenate((x_plot, np.flip(x_plot, 0)))\n",
    "err_ys = np.concatenate((mu_s + 2 * stds, np.flip(mu_s - 2 * stds, 0)))\n",
    "plt.fill_between(err_xs,err_ys,alpha=0.25,color=\"pink\")\n",
    "\n",
    "for i in range(3):\n",
    "    y_s=np.random.multivariate_normal(mu_s,Sigma_s)\n",
    "    plt.plot(x_plot,y_s,lw=1)\n",
    "plt.plot(x_plot,mu_s,lw=2,label=\"mean\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "回想一下Ridge回归\n",
    "$$w=\\mathop{argmin}_{w\\in\\mathbb R^d}\\lVert t-\\Phi w\\lVert^2_2+\\frac{1}{2}\\lVert\\lambda\\lVert^2$$\n",
    "令$$\\Phi\\Phi^T=k^T,C_N^{-1}=\\Phi\\Phi^T+\\frac{\\lambda^2}{2}$$\n",
    "ridge回归是一种最最最最简单的高斯过程回归，核函数就是简单的点积."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.4.3超参数的学习\n",
    "现在我们从数据中中推断预测时使用的核的超参数的值，考虑一个广泛使用的Sqared Exponential kernel：\n",
    "$$k(x_n,x_m)=\\theta_0exp\\{-\\frac{\\theta_1}{2}\\lVert x_n-x_m\\lVert^2\\}+\\theta_2+\\theta_3x_n^Tx_m$$\n",
    "那么高斯过程的对数似然函数:$$lnp(t|\\theta)=-\\frac{1}{2}ln|C_N|-\\frac{1}{2}t^TC_N^{-1}t-\\frac{N}{2}ln(2\\pi)$$\n",
    "对$\\theta|$求导就有:\n",
    "$$\\frac{\\partial}{\\partial\\theta_i}lnp(t|\\theta)=-\\frac{1}{2}Tr(C_N^{-1}\\frac{\\partial C_N}{\\partial \\theta_i})+\\frac{1}{2}t^TC_N^{-1}\\frac{\\partial C_N}{\\partial \\theta_i}C_N^{-1}t$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_toy_data(func, n=10, std=1., domain=[0., 1.]):\n",
    "    x = np.linspace(domain[0], domain[1], n)\n",
    "    t = func(x) + np.random.normal(scale=std, size=n)\n",
    "    return x, t\n",
    "\n",
    "def sinusoidal(x):\n",
    "        return np.sin(2 * np.pi * x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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mbp3KrF2zSLGk0KtaL0Y3GU3zMs3v+yFZXi5ePN3waUY0GMHqf1bzwdYPGP/neN7a+BYj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\nSZIkSUP+A4wDQpU2ygckAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f416096aa58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_train, y_train = create_toy_data(sinusoidal, n=7, std=0.1, domain=[0., 0.7])\n",
    "x = np.linspace(0, 1, 100)\n",
    "\n",
    "plt.figure(figsize=(20, 5))\n",
    "plt.subplot(1, 2, 1)\n",
    "model = GaussianProcessRegressor(kernel=RBF(np.array([1., 1.])), beta=100)\n",
    "model.fit(x_train, y_train)\n",
    "y, y_std = model.predict(x, with_error=True)\n",
    "plt.scatter(x_train, y_train, facecolor=\"none\", edgecolor=\"b\", color=\"blue\", label=\"training\")\n",
    "plt.plot(x, sinusoidal(x), color=\"g\", label=\"sin$(2\\pi x)$\")\n",
    "plt.plot(x, y, color=\"r\", label=\"gpr {}\".format(model.kernel.params))\n",
    "plt.fill_between(x, y - y_std, y + y_std, alpha=0.5, color=\"pink\", label=\"std\")\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "model.fit(x_train, y_train, iter_max=100)\n",
    "y, y_std = model.predict(x, with_error=True)\n",
    "plt.scatter(x_train, y_train, facecolor=\"none\", edgecolor=\"b\", color=\"blue\", label=\"training\")\n",
    "plt.plot(x, sinusoidal(x), color=\"g\", label=\"sin$(2\\pi x)$\")\n",
    "plt.plot(x, y, color=\"r\", label=\"gpr {}\".format(np.round(model.kernel.params, 2)))\n",
    "plt.fill_between(x, y - y_std, y + y_std, alpha=0.5, color=\"pink\", label=\"std\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.4.5 基于分类的高斯过程\n",
    "\n",
    "目标变量$t\\in{0,1}$,服从伯努力分布$p(t|a)=\\sigma(a)^t(1-\\sigma(a))^(1-t)$,需要确定预测分布$p(t_{N+1}|t)$,引入高斯先验:$p(a_{N+1})=\\mathcal N(a_{N+1}|0,C_{N+1})$\n",
    "\n",
    "$$p(t_{N+1}=1|t_N)=\\int p(t_{N+1}=1|a_{N+1})p(a_{N+1}|t_N)da_{N+!}$$\n",
    "求解方法:变分法，期望传播，Laplace近似。"
   ]
  }
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